For example, JP 10-48180 A, which corresponds to U.S. Pat. No. 6,120,677, describes a technology for detecting the impedance of an element (element impedance) of an oxygen concentration sensor that is used for controlling an air fuel ratio of an internal combustion engine. In the technology of JP 10-48180 A, a cell as the element is applied with a constant current for measuring an impedance, that is, for measuring a resistance value. A difference between a both-end voltage of the element before being applied with the constant current and a both-end voltage of the element after being applied with the constant current is detected as a value that is correlated with the impedance of the element.